Incremental Binding Energies Research Articles

Breakdown of the correlation between oxidation states and core electron binding energies at the sub-nanoscale

X-ray photoelectron spectroscopy is a powerful analytical tool to fingerprint the atomic oxidation state. However, the well-established trend that is found for bulk, ultra-thin films and surface oxides, which is usually characterized by an incremental binding energy shift upon increasing oxidation state, may not apply at the sub-nanoscale where reduced dimensionality and quantum size effects play a relevant role. Here we investigate through a combined experimental and theoretical approach the oxidation of size-selected Ag7 and Ag11 clusters supported on graphene, revealing an anomalous Ag 3d5/2 core level shift trend upon increasing O coverage. We show that the negative core level shift trend typical of Ag reverts back in the case of the highest Ag(III) oxidation state, an effect that is due to the peculiar electronic structure of Ag nano-oxides. Our results highlight the great care needed to extend at the zero-dimensional scale the knowledge acquired for the spectral interpretation of 3D and 2D materials.

Structures and Stabilities of Carbon Chain Clusters Influenced by Atomic Antimony.

The C-C bond lengths of the linear magnetic neutral CnSb, CnSb+ cations and CnSb- anions are within 1.255-1.336 Å, which is typical for cumulene structures with moderately strong double-bonds. In this report, we found that the adiabatic ionization energy (IE) of CnSb decreased with n. When comparing the IE~n relationship of CnSb with that of pure Cn, we found that the latter exhibited a stair-step pattern (n ≥ 6), but the IE~n relationship of CnSb chains took the shape of a flat curve. The IEs of CnSb were lower than those of corresponding pure carbon chains. Different from pure carbon chains, the adiabatic electron affinity of CnSb does not exhibit a parity effect. There is an even-odd alternation for the incremental binding energies of the open chain CnSb (for n = 1-16) and CnSb+ (n = 1-10, when n > 10, the incremental binding energies of odd (n) chain of CnSb+ are larger than adjacent clusters). The difference in the incremental binding energies between the even and odd chains of both CnSb and pure Cn diminishes with the increase in n. The incremental binding energies for CnSb- anions do not exhibit a parity effect. For carbon chain clusters, the most favorable binding site of atomic antimony is the terminal carbon of the carbon cluster because the terminal carbon with a large spin density bonds in an unsaturated way. The C-Sb bond is a double bond with Wiberg bond index (WBI) between 1.41 and 2.13, which is obviously stronger for a carbon chain cluster with odd-number carbon atoms. The WBI of all C-C bonds was determined to be between 1.63 and 2.01, indicating the cumulene character of the carbon chain. Generally, the alteration of WBI and, in particular, the carbon chain cluster is consistent with the bond length alteration. However, the shorter C-C distance did not indicate a larger WBI. Rather than relying on the empirical comparison of bond distance, the WBI is a meaningful quantitative indicator for predicting the bonding strength in the carbon chain.

Vacancy clustering behaviors and stable configurations in vanadium metal: First-principles investigations

• We calculate energetics and configurations of vacancy clusters with the size up to 30 in vanadium. • The average formation energies of vacancy clusters decrease with the size. • We determined the relationship between energetics of vacancy clusters and Wigner-Seitz area in vanadium. • We establish a model by machine learning to predict formation energies of vacancy clusters. The clustering behaviors and stable configurations of vacancies with the size up to 30 in vanadium were studied by first-principles investigations. The average formation energies per vacancy of vacancy clusters decreases with the sizes. When V n cluster with the odd size forms V n +1 cluster, the average formation energy per vacancy has a lager reduction relative to the case of even size. The stabilities of vacancy clusters increase with the sizes in terms of the total binding energy ( n =2-30), the incremental binding energies of vacancy clusters show an increasing trend of fluctuation with the sizes, which can be explained by both the size characteristics and terrace-ledge-kink model. We also estimated the relationship between vacancy formation/incremental binding energy and Wigner-Seitz area. Finally, we established a machine learning model based on Linear-SVM to predict formation energies of larger vacancy clusters. These results deepened the understanding of the formation and evolution of nanovoids in vanadium metal under irradiation.

Superatomic Signature and Reactivity of Silver Clusters with Oxygen: Double Magic Ag 17 – with Geometric and Electronic Shell Closure

Understanding the stability and reactivity of silver clusters toward oxygen provides insights to design new materials of coinage metals with atomic precision. Herein, we report a systematic study o...

Structural Evolution and Electronic Properties of TaSin-/0 (n = 2-15) Clusters: Size-Selected Anion Photoelectron Spectroscopy and Theoretical Calculations.

The structural evolution and electronic properties of TaSin-/0 (n = 2-15) clusters are explored using anion photoelectron spectroscopy accompanied by quantum chemical calculations. The Ta atom in TaSin-/0 is inclined to interact with more Si atoms and has high coordination numbers. The theoretical calculations show that TaSi2-/0 have trianglur structures and TaSi3-/0 adopt pyramid structures, while the geometries of TaSin-/0 (n = 4-7) are all exohedral structures dominated by bipyramid-based configurations with the Ta atom face-capping the Sin motifs. TaSi8-/0 and TaSi9-10- have boat-shaped geometries, whereas TaSi9-10 neutrals adopt bipyramid-based geometries instead of boat-shaped ones. TaSi11- and TaSi12 are confirmed as the critical size of transiting from exohedral to endohedral structures for anionic and neutral clusters, respectively. TaSi12-15-/0 have pentagonal or hexagonal prism-based geometries. Natural population analysis shows that the electron transfers from Sin skeletons to Ta atom. The second-order energy differences (Δ2E) and incremental binding energy (ΔEI) values exhibit strong odd-even alternations, suggesting that the TaSin-odd-/0 clusters are more stable than the adjacent TaSin-even-/0 ones, except that TaSi12-/0 are more stable than TaSi11-/0 and TaSi13-/0.

Structural evolution from exohedral to endohedral geometries, dynamical fluxionality, and structural forms of medium-sized anionic and neutral Au2Sin (n = 8-20) clusters.

The structural evolution of medium-sized anionic and neutral Au2Sin (n = 8-20) clusters is investigated by using density functional theory (DFT) calculations and CCSD(T) methods in combination with the particle swarm optimization (CALYPSO) global search algorithm. The geometries of anionic and neutral Au2Sin clusters change from exohedral to endohedral ones with the increasing cluster sizes, and the critical size of forming Au2-endohedral structures for both anionic and neutral clusters is confirmed to be n = 20, in which a C2h symmetric Au2-endohedral cage-like structure is observed. Anionic and neutral Au2Sin clusters are primarily dominated by prism-based geometries with most of them adopting different structural features. It is found that the two Au atoms prefer to occupy low coordination sites and interact with fewer Si atoms. The Au atoms carry negative charges because of the electron-transfer from Sin frameworks. Meanwhile, the two Au atoms have very weak interactions. The second-order energy differences and incremental binding energies of anionic and neutral Au2Sin clusters exhibit an odd-even alternation and Au2Si20-/0 clusters are proven to have the highest chemical stability among these Au-Si clusters. Interestingly, Au2Si8-, Au2Si9-, Au2Si13-, Au2Si15-, and Au2Si17- anions, along with Au2Si13, Au2Si14, and Au2Si17 neutrals, have multiplicity of structural forms and their low-lying isomers show dynamical fluxionality due to the low barrier energies.

Th doped carbon clusters ThCn (n = 1–7): Stability and bonding natures

The hybrid HF/DFT functionals in conjunction with small-core pseudopotential have been employed to investigate the geometric and electronic structures of small ThCn (n = 1–7) clusters. The fan-type isomers were found to be more stable than the linear ones. Analyses on the incremental binding energies indicate that the clusters with even C atoms possess the higher stability than odd-numbered ones. The interaction natures of Th-C chemical bonds were revealed by the methods of bond overlap density of states (OPDOS), adaptive natural density partitioning (AdNDP) and electron localization function (ELF).

Nature of bonding and cooperativity in linear DMSO clusters: A DFT, AIM and NCI analysis

This study aims to cast light on the nature of interactions and cooperativity that exists in linear dimethyl sulfoxide (DMSO) clusters using dispersion corrected density functional theory. In the linear DMSO, DMSO molecules in the middle of the clusters are bound strongly than at the terminal. The plot of the total binding energy of the clusters vs the cluster size and mean polarizabilities vs cluster size shows an excellent linearity demonstrating the presence of cooperativity effect. The computed incremental binding energy of the clusters remains nearly constant, implying that DMSO addition at the terminal site can happen to form an infinite chain. In the linear clusters, two σ-hole at the terminal DMSO molecules were found and the value on it was found to increase with the increase in cluster size. The quantum theory of atoms in molecules topography shows the existence of hydrogen and SO⋯S type in linear tetramer and larger clusters. In the dimer and trimer SO⋯OS type of interaction exists. In 2D non-covalent interactions plot, additional peaks in the regions which contribute to the stabilization of the clusters were observed and it splits in the trimer and intensifies in the larger clusters. In the trimer and larger clusters in addition to the blue patches due to hydrogen bonds, additional, light blue patches were seen between the hydrogen atom of the methyl groups and the sulphur atom of the nearby DMSO molecule. Thus, in addition to the strong H-bonds, strong electrostatic interactions between the sulphur atom and methyl hydrogens exists in the linear clusters.

Density functional theory of InCn+(n=110) clusters

Small indium-doped carbon clusters InCn+(n=110) are systematically studied by the density functional theory at the B3 LYP/LANL2 DZ level. The computed properties include equilibrium geometries, electronic energies, vibrational frequencies, dipole moments and rotational constants for individual species. The calculation results show that the open-chain linear isomers with the indium atom bound to the end of the carbon chain are the most stable geometry in all cases. There must exist a cyclic or fan structure in the metastable or the third stable structure of cluster. The bigger the size of the cluster, the more obvious the stability of the structure is. The electronic ground state is found to be alternately a triplet for even n and a singlet for odd n with the only exception of InC+. It is generally observed that the spin contamination is not serious for all electronic ground states because the s2 values are uniform and in general deviate slightly from the pure spin values, and the B3 LYP wave functions are nearly spin-pure. It is also found that in the lowest-energy linear structure, the InC bond is longer (from 2.319 to 2.850 ) than the corresponding CC bonds in a range from 1.268 to 1.360 . The CC distances can be assimilated to moderately strong double bonds underlying a clear bonding in the corresponding structures. In addition, we observe a clear alternation in CC distances. The CoddCeven distances are shorter than the CevenCodd ones which mainly results from the charge distribution and spin density. According to the calculation and analysis of the incremental binding energy and the second difference we can deduce an even-odd alternation in the cluster stability for the linear InCn+, with their n-odd members being more stable than the adjacent even-numbered ones. This parity effect also appears in the adiabatic ionization potential curves. The analysis of magnetic properties shows the even-odd alternation with n-even clusters presenting higher values of magnetic moment than n-odd ones. The study of the polarizability indicates that the average values of both the polarization tensors and the anisotropic invariants increase with the size of cluster increasing.

Seventeen‐Coordinate Actinide Helium Complexes

AbstractThe geometries and electronic structures of molecular ions featuring He atoms complexed to actinide cations are explored computationally using density functional and coupled cluster theories. A new record coordination number is established, as AcHe173+, ThHe174+, and PaHe174+are all found to be true geometric minima, with the He atoms clearly located in the first shell around the actinide. Analysis of AcHen3+(n=1–17) using the quantum theory of atoms in molecules (QTAIM) confirms these systems as having closed shell, charge‐induced dipole bonding. Excellent correlations (R2>0.95) are found between QTAIM metrics (bond critical point electron densities and delocalization indices) and the average Ac−He distances, and also with the incremental He binding energies.

Seventeen-Coordinate Actinide Helium Complexes.

The geometries and electronic structures of molecular ions featuring He atoms complexed to actinide cations are explored computationally using density functional and coupled cluster theories. A new record coordination number is established, as AcHe173+ , ThHe174+ , and PaHe174+ are all found to be true geometric minima, with the He atoms clearly located in the first shell around the actinide. Analysis of AcHen3+ (n=1-17) using the quantum theory of atoms in molecules (QTAIM) confirms these systems as having closed shell, charge-induced dipole bonding. Excellent correlations (R2 >0.95) are found between QTAIM metrics (bond critical point electron densities and delocalization indices) and the average Ac-He distances, and also with the incremental He binding energies.

Structures and properties of the potassium-doped carbon clusters KCn/KCn +/KCn −(n = 1−10)

A systematic density functional theory study of the potassium-doped small carbon clusters KC n /KC + /KC − (n = 1−10) has been carried out using B3LYP method with 6–311+G* basis set. Several properties including equilibrium geometries, electronic states, relative energies, ionization potentials and electron affinities have been investigated for linear and cyclic isomers. The stability of different structures and states has been discussed according to the relative energy for the same size, and the incremental binding energy for different size. For neutral KC n and cationic KC + clusters, their lowest-lying states mainly have linear structure, while for anionic KC − , they all have fan-like lowest-energy structure, except KC−, KC 3 − , and KC 10 − . The KC n /KC + /KC − clusters have been compared with iso-valent systems LiC n /LiC + /LiC − , NaC n /NaC + /NaC − , and CsC − , and the differences are discussed.

Theoretical studies on the structures and electronic spectra of carbon chains C n N (n = 3–12)

A theoretical study of the linear nitrogen-terminated carbon chains CnN (n = 3–12) is carried out with density functional theories and ab initio methods. All species in the ground state are fully optimized with the B3LYP, CAM-B3LYP, and RCCSD(T) calculations. The present results reveal that the carbon radicals under study possess stable structures with the X2Σ+ ground-state symmetry for CnN (n = 3, 5) or X2Π for the rest members in the series. According to the trends of odd/even alternation in energy differences and incremental binding energies, it is clear that the n-odd CnN chains are relatively more stable than n-even ones. Furthermore, the electronic spectra of CnN (n = 3–12) are investigated by means of CASPT2 method. The predicted vertical excitation energies from the ground state to the low-lying excited states basically agree well with the available experimental observations. In addition, by performing curve fittings, the vertical excitation energies of the transitions from the ground states (X2Σ+ or X2Π) to the low-lying excited state 22Π for the odd members are found to obey a nonlinear ΔE–n relationship as a function of chain size, matching the experimental findings well. Moreover, the strongest absorption band for the even series shows a nonlinear trend of biexponential decay.

Exploration on the structure, stability, and isomerization of planar C n B5 (n = 1−7) clusters

The structures, stabilities, nature of bonding, and potential energy surfaces of low-energy isomers of planar CnB5 (n = 1−7) have been systematically explored at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d) level. Incremental binding energy (IBE) and second order energy difference (Δ2E) analyses demonstrate that CnB5 clusters with even n have relatively higher stability. The nature of bonding in these clusters is discussed based on valence molecular orbital (VMO), and Mayer bond order (MBO). Hückel (4n + 2) rule and nucleus-independent chemical shift (NICS) values suggest that the ground states of C3B5, C4B5, and C7B5 have π aromaticity. VMO, electron localization function (ELF), adaptive natural density partitioning (AdNDP), and NICS analyses reveal the double aromaticity of C3B5 cation. CB5 and C3B5 are stable both thermodynamically and kinetically based on isomerization analysis. In addition, the simulated IR spectra are expected to be helpful for future experimental studies of these clusters.

Geometry, stability, and isomerization of B n N2 (n = 1−6) isomers

We perform a systematic study on the geometry, stability, nature of bonding, and potential energy surface of low-lying isomers of planar and cyclic BnN2 (n = 1−6) at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d) level. BnN2 (n = 2−4) clusters are structurally similar to pure boron clusters. The evolution of the binding energy per atom, incremental binding energy, and second-order difference of total energy with the size of BnN2 reveals that the lowest energy isomer of B3N2 has high stability. B5N2 and B6N2 possess π-aromaticity according to Hückel (4n + 2) rule. The aromaticity of some isomers of B4N2 and B6N2 is examined based on their valence molecular orbitals. At the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d) level, several B2N2, B3N2, B4N2, and B5N2 isomers are predicted to be stable both thermodynamically and kinetically, and detectable in future experiments. © 2013 Wiley Periodicals, Inc.

Aqueous microsolvation of HgClOH. A systematic MP2 study of the HgClOH–(H2O)n species with n = 1–4

We report a systematic study of aqueous microsolvation of HgClOH. The optimized structures, harmonic vibrational frequencies and binding energies of one to four water molecules coordinated with HgClOH have been computed with 2nd order Möller–Plesset perturbation theory. Accurate incremental water binding energies have been obtained at the complete basis set (CBS) limit using sequences of augmented correlation-consistent basis sets including the counterpoise correction. The main water-solute interactions arise from hydrogen bonding and hydrogen–halogen bonds. Although mercury establishes two direct orbital-driven interactions with water oxygens for n=3 and n=4, the intramolecular geometry of HgClOH is barely modified by the microsolvation environment. The CP-corrected MP2/CBS incremental binding energies are 5.20, 11.49, 6.63 and 10.00kcal/mol for n=1–4. The structural and vibrational analysis reveal that the strongest water-solute interaction appears for n=3.

Au-doped carbon clusters AuC n with n = 1–11: a theoretical investigation

The hybrid HF/DFT method B3LYP has been employed to investigate the geometrical and electronic structures of AuCn (n = 1–11) clusters. The properties such as geometrical parameters and electronic energies are determined for open-chain and cyclic species. Our results indicate that the open-chain structures with low spin states (doublet) are more stable than the cyclic ones for the small sizes clusters (n ≤ 9), as the cluster sizes increase (n = 10, 11), the cyclic species are more stable. The incremental binding energies show a smooth even–odd alternation phenomenon for open-chain species, n-even (n is the numbers of C atom in the clusters) species have the stronger stabilities relative to the adjacent odd-numbered ones. In addition, the most favorable dissociation channels are determined by calculating the fragmentation energies accompanying various possible pathways. The studied clusters incline to be dissociated to Au + Cn and AuCn−3 + C3 fragments.

Structures and stabilities of GaCn (n = 1–10) clusters

A theoretical study of the small Gallium-doped carbon clusters GaCn (n=1–10) has been studied with density functional theory (DFT) method at the B3LYP/6-311+G* level. The computed properties include equilibrium geometries, electronic energies, vibrational frequencies, dipole moments, and rotational constants for individual species. According to these calculations, except for smaller GaC2, the open-chain linear or quasi-linear isomers with the Gallium atom bound to the end of the carbon chain are the most stable geometry in all cases. The electronic ground state is found to be a doublet state for the GaCn clusters, with the only exception of the smallest GaC. The incremental binding energy diagram shows a strong even–odd alternation in the cluster stability for these linear GaCn, with their n-even members being much more stable than the adjacent odd-numbered ones. These parity effects also appear in the second difference in energy curves. In addition, by comparing with the fragmentation energies accompanying various channels, the most favorable dissociation channels are acquired.

Theoretical studies on structures and electronic spectra of linear free radicals CnH (n = 5–12)

The B3LYP, CAM-B3LYP, and coupled cluster CCSD(T) calculations have been utilized to determine the equilibrium structures of linear carbon radicals CnH (n=5–12) in their ground states, as well as the CASSCF method used to optimize the ground and selected low-lying excited states. DFT-calculations show that even-n radicals C2nH have polyacetylene-like structures with significant single-triple bond length alternation, whereas the odd-numbered analogues C2n+1H exhibit a trend from polyacetylene-like characters into cumulenic-like arrangement towards C ends along the carbon chains. The stabilities of the system under study have been evaluated by analyses of the vibrational frequencies and incremental binding energies. For the whole CnH (n=5–12) series, the vertical excitation energies and oscillator strengths have been calculated at the CASPT2/cc-pVTZ level of theory. At the B3LYP optimized geometries, the lowest 12Δ←X2Π transitions for C5H and C7H occur at 2.36 and 2.14eV, respectively, comparing well with the observed values of 2.33 and 2.09eV. Moreover, the strongest 22Π←X2Π transitions for C2nH (n=3–6) are predicted to be at 2.39, 2.00, 1.80, and 1.64eV, respectively, which are in agreement with the experimental observations. Additionally, the possible dissociation channels and the fragmentation energies of CnH (n=5–12) series are discussed in the paper.

On the structures, stabilities, and potential energy surfaces of planar BnN (n = 1–6) clusters

The structures, stabilities, and potential energy surfaces (PESs) of the low-lying isomers of planar BnN (n=1–6) clusters are searched at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d) level. The lowest-energy structures (1a–6a) of planar BnN (n=1–6) are located. It is worthy to note a structural transition occurring in the series of BnN (n=1–6) clusters upon increase of the boron content from n=3 to n=4. The evolution of the binding energy per atom, incremental binding energy, and second order difference of total energy with the size of BnN reveals that the lowest-energy isomers 2a (B2N) and 5a (B5N) are highly stable. Results demonstrate that the stability of lowest-energy isomers of BnN (n=1–6) is attributed to the delocalized π, σ-radial, and σ-tangential molecular orbitals (MOs) interactions. The isomers of BnN (n=4–6) with planar multicoordinate boron or nitrogen are unfavorable in energy. The double aromaticity of isomer 3d of B3N is discussed in terms of valence molecular orbital, electron localization function (ELF) and adaptive natural density partitioning (AdNDP), and NICS analyses. Interestingly, some isomer pairs can be transferred directly to each other by two or three isomerization channels. Some isomers of BnN with large thermodynamic and kinetic stability are predicted in terms of their total energies and potential energy surfaces, which is important for future experimental studies.